Title:
|
Backstepping based nonlinear adaptive control for the extended nonholonomic double integrator (English) |
Author:
|
Abbasi, Waseem |
Author:
|
ur Rehman, Fazal |
Author:
|
Shah, Ibrahim |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 (print) |
ISSN:
|
1805-949X (online) |
Volume:
|
53 |
Issue:
|
4 |
Year:
|
2017 |
Pages:
|
578-594 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
In this paper a steering control algorithm for the Extended Nonholonomic Double Integrator is presented. An adaptive backstepping based controller is proposed which yields asymptotic stabilization and convergence of the closed loop system to the origin. This is achieved by transforming the original system into a new system which can be globally asymptotically stabilized. Once the new system is stabilized, the stability of the original system can be easily established. Stability of the closed loop system is analyzed on the basis of Lyapunov theory. The effectiveness of the proposed control algorithm is verified through numerical simulation and the results are compared to existing methods. (English) |
Keyword:
|
nonholonomic systems |
Keyword:
|
feedback stabilization |
Keyword:
|
systems with drift |
Keyword:
|
adaptive backstepping |
Keyword:
|
Lyapunov function |
MSC:
|
93D15 |
idZBL:
|
Zbl 06819625 |
idMR:
|
MR3730253 |
DOI:
|
10.14736/kyb-2017-4-0578 |
. |
Date available:
|
2017-11-12T09:52:41Z |
Last updated:
|
2023-10-03 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146945 |
. |
Reference:
|
[1] Abbassi, W., Rehman, F.: Adaptive integral sliding mode stabilization of nonholonomic drift-free systems..Math. Problems Engrg. 2016 (2016), 1-11. MR 3576111, 10.1155/2016/9617283 |
Reference:
|
[2] Aguiar, A. P., Atassi, A. N., Pascoal, A. M.: Regulation of a nonholonomic dynamic wheeled mobile robot with parametric modeling uncertainty using Lyapunov functions..In: Proc. 39th IEEE Conference on Decision and Control 3 (2000), 2995-3000. 10.1109/cdc.2000.914276 |
Reference:
|
[3] Aguiar, A. P., Pascoal, A. M.: Stabilization of the extended nonholonomic double integrator via logic-based hybrid control..IFAC Proc. Vol. 33 (2000), 27, 351-356. 10.1016/s1474-6670(17)37954-5 |
Reference:
|
[4] Astolfi, A.: Discontinuous control of the Brockett integrator..Europ. J. Control, 1, (1998), 49-63. 10.1016/s0947-3580(98)70099-8 |
Reference:
|
[5] Bloch, A., Drakunov, S.: Stabilization and tracking in the nonholonomic integrator via sliding modes..Systems Control Lett. 2 (1996), 91-99. MR 1420406, 10.1016/s0167-6911(96)00049-7 |
Reference:
|
[6] Brockett, R. W.: Asymptotic stability and feedback stabilization..In: Differential Geometric Control Theory (R. W. Brockett, R. S. Millman, and H. J. Sussman, eds.), Birkhauser, Boston 1983, pp. 181-191. Zbl 0528.93051, MR 0708502 |
Reference:
|
[7] Dixon, W. E., Jiang, Z. P., Dawson, D. M.: Global exponential setpoint control of wheeled mobile robots: A Lyapunov approach..In: Proc. 39th IEEE Conference on Decision and Control 2 (1999), 265-279. MR 1833045 |
Reference:
|
[8] Escobar, G., Ortega, R., Reyhanoglu, M.: Regulation and tracking of the nonholonomic double integrator: A field-oriented control approach..Automatica 1 (1998), 125-131. MR 1614117, 10.1016/s0005-1098(97)00155-6 |
Reference:
|
[9] Fang, F., Wei, L.: Backstepping-based nonlinear adaptive control for coal-fired utility boiler-turbine units..Appl. Energy 3 (2011), 814-824. 10.1016/j.apenergy.2010.09.003 |
Reference:
|
[10] Godhavn, J-M., Egeland, O.: A Lyapunov approach to exponential stabilization of nonholonomic systems in power form..IEEE Trans. Automat. Control 7 (1997), 1028-1032. MR 1469849, 10.1109/9.599989 |
Reference:
|
[11] Jiang, Z. P., Nijmeijer, H.: A recursive technique for tracking control of nonholonomic systems in chained form..In: Proc. 39th IEEE Conference on Decision and Control 2 (1999), 265-279. MR 1669982, 10.1109/9.746253 |
Reference:
|
[12] Kolmanovsky, I., McClamroch, N. H.: Developments in nonholonomic control problems..IEEE Control Syst. 6 (1995), 20-36. 10.1109/37.476384 |
Reference:
|
[13] Morin, P., Samson, C.: Control of Nonlinear Chained Systems: From the Routh-Hurwitz Stability Criterion to Time-Varying Exponential Stabilizers..Springer 2000. MR 1741954 |
Reference:
|
[14] Pascoal, A. M., Aguiar, A. P.: Practical stabilization of the extended nonholonomic double integrator..In: Proc. 10th Mediterranean Conferenceon Control and Automation, 2002. |
Reference:
|
[15] Pomet, J. B.: Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift..Systems Control Lett. 2 (1992), 147-158. MR 1149359, 10.1016/0167-6911(92)90019-o |
Reference:
|
[16] Rehman, F.: Steering control of nonholonomic systems with drift: The extended nonholonomic double integrator example..Nonlinear Analysis Theory Methods Appl. 8 (2005), 1498-1515. MR 2164937, 10.1016/j.na.2005.03.086 |
Reference:
|
[17] Sun, L.-Y., Tong, S., Liu, Y.: Adaptive backstepping sliding mode H infinity control of static var compensator..IEEE Trans. Control Systems Technol. 5 (2011), 1178-1185. 10.1109/tcst.2010.2066975 |
Reference:
|
[18] Wang, Z., Li., S., Fei, S.: Finite-time tracking control of a nonholonomic mobile robot..Asian J. Control 3 (2009), 344-357. 10.1002/asjc.112 |
Reference:
|
[19] Zhou, J., Wen, C.: Adaptive Backstepping Control of Uncertain Systems: Nonsmooth Nonlinearities, Interactions or Time-Variations..Springer 2008. MR 2391666 |
. |